On self-similar spectral measures

摘要

A probability measure mu on R is called a spectral measure if it has an exponential orthogonal basis for L-2 (mu). In this paper, we study the spectrality of the self-similar measure generated by an iterated function system {tau d(.) = rho( + d)}(d is an element of D )dED associated with a real number 0 < rho < 1 and a finite set D subset of R. It can also be expressed as